Defects in spherical rolling element bearings are the most studied bearing defects in laboratory settings. A commonly available REB (rolling element bearing) is an assembly of Outer race, Inner race, Spherical balls, and a cage holding these rolling elements. The complex dynamic interaction of such moving elements imparts strong nonlinear characteristics to the output of bearings (both healthy and defective). In that case, diagnosis of the faults in bearings is challenging as the defect signals get mixed with signals of different interfering components plus the inherent nonlinearities of the bearings.
There are three broad categories in which a fault signal can be decomposed for analysis:
1.Time domain.
2.Frequency domain.
3.Time-frequency domain

Common defects in rolling element bearings, Parts of rolling element bearings

As the name suggests time domain analysis involves extracting information from time signals (peak, rms, crest factor, kurtosis etc.) whereas in frequency domain we look for changes in specific frequencies which may correspond to the defective part of the bearing.
The main types of defects for typical REB (as shown in figure above) generally vibrate with their characteristic frequencies given as:

Where, 𝑛 – nomber of rolling elements
𝑓𝑟– rotating speed
ϕ– load angle
D, d – diameter of the cage and rolling elements respectively.

However, there is considerable slip between the rolling components hence these kinematic frequecies change considerably. Thus to overcome these difficulties the signal is further processed using envelope analysis, minimum entropy deconvolution, HH transform, etc. to extract fault characteristics. In applying each of these techniques there is an assumption regarding the type of fault, operating conditions, sensing methodology and thus how the final signal is modified in case a defect exists.

Our lab uses expertise in machine learning, signal processing, and nonlinear dynamics to incorporate the above knowledge of the system to develop innovative algorithms for fault diagnosis.

The digital objective identifiers (DOI) of some related papers which have utilized the above approach:

1. Kappaganthu, K., and Nataraj, C. (September 9, 2011)."Feature Selection for Fault Detection in Rolling Element Bearings Using Mutual Information."ASME. J. Vib. Acoust. December 2011;
2. 10.1016/j.cnsns.2011.02.001"Feature Selection for Fault Detection in Rolling Element Bearings Using Mutual Information."ASME. J. Vib. Acoust. December 2011;
3. Haj Mohamad, T., Samadani, M., and Nataraj, C. (May 14, 2018)."Rolling Element Bearing Diagnostics Using Extended Phase Space Topology."ASME. J. Vib. Acoust. December 2018;
4. Haj Mohamad, T, Kitio Kwuimy, CA, & Nataraj, C."Discrimination of Multiple Faults in Bearings Using Density-Based Orthogonal Functions of the Time Response."Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 29th Conference on Mechanical Vibration and Noise. Cleveland, Ohio, USA. August 6–9, 2017. V008T12A035. ASME.
5. Zhu, Z, & Du, X. "A System Reliability Method With Dependent Kriging Predictions."Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2B: 42nd Design Automation Conference. Charlotte, North Carolina, USA. August 21–24, 2016. V02BT03A043. ASME.